Figured it out. I was in talk with Andy over at Ultimarc since I posted about the new problem - I posted here in case someone had encountered the same thing and could skip over troubleshooting straight to the solution. An unlikely hope, but never something not worth looking into.
Anyhow, the problem is that the board had somehow gotten put into Xinput Mode 3, which maintains specific mapping. It needed to be in Xinput Mode 5. Trouble is, I couldn't get it to go into Mode 5. As I noted in my most recent post, it wouldn't switch modes at all! THAT part turned out to be a simple case of PEBCAK - I had accidentally clicked off the Ipac Shift function for the START1 button at some point - since my setup only ever would need that to change input Modes, easy error for me to overlook. But after correcting this, it still wouldn't go into Xinput Mode 5.
On a hunch, I switched to Dinput Mode 2, then tried switching back to Xinput Mode 5, and... it switched over! After doublechecking my mappings to make sure they were as needed, I powered off the PC, and when it powered back on, the intended mappings remained!
So, what I SUSPECT, and I have asked Andy if he thinks this could be the case, is that the prior weird behavior from Steam (the one that led to this thread) caused the system to get locked into Mode 3 while THINKING it was in Mode 5, so it wouldn't reconfigure itself into Mode 5 until it was taken out of it. I'll post Andy's opinion on that when he gets back to me.